Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring

Abstract

A ten-dimensional super-Poincare covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincare covariant prescription was defined for computing tree amplitudes and was shown to coincide with the standard RNS prescription. In this paper, picture-changing operators are used to define functional integration over the pure spinor ghosts and to construct a suitable $b$ ghost. A super-Poincare covariant prescription is then given for the computation of N-point multiloop amplitudes. One can easily prove that massless N-point multiloop amplitudes vanish for N<4, confirming the perturbative finiteness of superstring theory. One can also prove the Type IIB S-duality conjecture that $R^4$ terms in the effective action receive no perturbative contributions above one loop.

45 pages harvmac tex, added minor clarifications

Cited by in corpus (143)

• Pure Spinor Formalism as an N=2 Topological String
• Duality and higher derivative terms in M theory
• Equivalence of Two-Loop Superstring Amplitudes in the Pure Spinor and RNS Formalisms
• The closed-string 3-loop amplitude and S-duality
• R^4, purified
• Super-Poincare Covariant Two-Loop Superstring Amplitudes
• Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
• New Higher-Derivative $R^4$ Theorems
• Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism
• The Structure of n-Point One-Loop Open Superstring Amplitudes
• 5 loops in 24/5 dimensions
• Some Superstring Amplitude Computations with the Non-Minimal Pure Spinor Formalism
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Multiparticle one-loop amplitudes and S-duality in closed superstring theory
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• Relating the Green-Schwarz and Pure Spinor Formalisms for the Superstring
• Non-linear gauge transformations in $D=10$ SYM theory and the BCJ duality
• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• Origin of Pure Spinor Superstring
• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
• Simplifying the Tree-level Superstring Massless Five-point Amplitude
• The Overall Coefficient of the Two-loop Superstring Amplitude Using Pure Spinors
• Pure spinor superfields -- an overview
• Pure Spinor Superspace Identities for Massless Four-point Kinematic Factors
• Tree-level amplitudes from the pure spinor superstring
• Supergravity Actions with Integral Forms
• Double-Copy Structure of One-Loop Open-String Amplitudes
• Explaining the Pure Spinor Formalism for the Superstring
• Y-formalism and $b$ ghost in the Non-minimal Pure Spinor Formalism of Superstrings
• Spinor Fields Classification in Arbitrary Dimensions and New Classes of Spinor Fields on 7-Manifolds
• The Character of Pure Spinors
• Six Open String Disk Amplitude in Pure Spinor Superspace
• The Geometry of Supermanifolds and New Supersymmetric Actions
• Higher genus superstring amplitudes from the geometry of moduli spaces
• Towards Field Theory Amplitudes From the Cohomology of Pure Spinor Superspace
• All-order differential equations for one-loop closed-string integrals and modular graph forms
• Y-formalism in Pure Spinor Quantization of Superstrings
• Duality completion of higher derivative corrections
• Four-Point One-Loop Amplitude Computation in the Pure Spinor Formalism
• Two-Loop Superstrings VII, Cohomology of Chiral Amplitudes
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Towards the n-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure
• Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings
• The One-loop Open Superstring Massless Five-point Amplitude with the Non-Minimal Pure Spinor Formalism
• Superstring loop amplitudes from the field theory limit
• Superstrings in AdS
• Tetrahedral modular graph functions
• A Note on the Classical BRST Symmetry of the Pure Spinor String in a Curved Background
• From maximal to minimal supersymmetry in string loop amplitudes
• Towards the n-point one-loop superstring amplitude II: Worldsheet functions and their duality to kinematics
• Towards the n-point one-loop superstring amplitude I: Pure spinors and superfield kinematics
• On the absence of BPS preonic solutions in IIA and IIB supergravities
• D=11 massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries
• One-loop Superstring Amplitude From Integrals on Pure Spinors Space
• Cech and de Rham Cohomology of Integral Forms
• Partition Functions of Pure Spinors
• Lower-dimensional pure-spinor superstrings
• The D^{10} R^4 term in type IIB string theory
• Spinor moving frame, M0-brane covariant BRST quantization and intrinsic complexity of the pure spinor approach
• Higher-loop amplitudes in the non-minimal pure spinor formalism
• On Cancellations of Ultraviolet Divergences in Supergravity Amplitudes
• Comments on BRST quantization of strings
• The cohomology of superspace, pure spinors and invariant integrals
• Evaluating one-loop string amplitudes
• The D^6 R^4 term in type IIB string theory on T^2 and U-duality
• S-matrix elements from T-duality
• Loop amplitudes in maximal supergravity with manifest supersymmetry
• Notes on the ambitwistor pure spinor string
• Nilpotency of the b ghost in the non-minimal pure spinor formalism
• BRST quantization of the pure spinor superstring
• The b Ghost of the Pure Spinor Formalism is Nilpotent
• Worldsheet factorization for twistor-strings
• Pure-spinor superstrings in d=2,4,6
• Two-loop superstring five-point amplitudes III, construction via the RNS formulation: even spin structures
• Local BCJ numerators for ten-dimensional SYM at one loop
• Ramond-Ramond corrections to type II supergravity at order ${\alpha }^{\prime 3}$
• D-Brane Boundary States in the Pure Spinor Superstring
• On S-duality of D${}_3$-brane S-matrix
• Spinor frame formalism for amplitudes and constrained superamplitudes of 10D SYM and 11D supergravity
• Pure Spinors, Free Differential Algebras, and the Supermembrane
• Brackets, Sigma Models and Integrability of Generalized Complex Structures
• Chern-Simons Theory on Supermanifolds
• On Lagrangian approach to self-dual gauge fields in spacetime of nontrivial topology
• First-quantized N=4 Yang-Mills
• S-duality of tree-level S-matrix elements in D${}_3$-brane effective action
• Counterterms in Gravity in the Light-Front Formulation and a D=2 Conformal-like Symmetry in Gravity
• Conquest of the ghost pyramid of the superstring
• One-Dimensional Super Calabi-Yau Manifolds and their Mirrors
• $A_{\infty }$-Algebra from Supermanifolds
• BRST Anomaly and Superspace Constraints of the Pure Spinor Heterotic String in a Curved Background
• Fermionic superstring loop amplitudes in the pure spinor formalism
• Notes on the pure spinor b ghost
• Worldline Approach of Topological BF Theory
• The geometry of pure spinor space
• Tree-level S-matrix elements from S-duality
• Theta Expansion of First Massive Vertex Operator in Pure Spinor
• Non-Critical Pure Spinor Superstrings
• S-duality invariant dilaton couplings at order ${\alpha }^{\prime 3}$
• On semiclassical analysis of pure spinor superstring in an AdS_5 x S^5 background
• Integrated Massive Vertex Operator in Pure Spinor Formalism
• Decoupling of unphysical states in the minimal pure spinor formalism I
• Note About Classical Dynamics of Pure Spinor String on AdS_5 x S_5 Background
• Fermionic one-loop amplitudes of the RNS superstring
• S-duality of color-ordered amplitudes
• A Note on T-dualities in the Pure Spinor Heterotic String
• On D-Brane Boundary State Analysis in Pure-Spinor Formalism
• S-duality constraint on higher-derivative couplings
• D=4 Pure Spinor Superstring and N=2 Strings
• One-loop superstring six-point amplitudes and anomalies in pure spinor superspace
• Ultraviolet divergences in maximal supergravity from a pure spinor point of view
• Pure Spinor b-ghost in a Super-Maxwell Background
• Super Quantum Mechanics in the Integral Form Formalism
• On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring
• Pure Spinor Approach to Type IIA Superstring Sigma Models and Free Differential Algebras
• DDF Construction and D-Brane Boundary States in Pure Spinor Formalism
• Decoupling of unphysical states in the minimal pure spinor formalism II
• Relating the $b$ ghost and the vertex operators of the pure spinor superstring
• Worldsheet dilatation operator for the $AdS$ superstring
• Non-minimal fields of the pure spinor string in general curved backgrounds
• On Projections to the Pure Spinor Space
• On the field-antifield (a)symmetry of the pure spinor superstring
• Wess-Zumino and Super Yang-Mills Theories in D=4 Integral Superspace
• On the Relation between Hybrid and Pure Spinor String Theory
• Note About Redefinition of BRST Operator for Pure Spinor String in General Background
• Pure spinor formulation of the superstring and its applications
• Black Hole Partition Function using Hybrid Formalism of Superstrings
• Canonical description of D=10 superstring formulated in supertwistor space
• Form factors from string amplitudes
• Free Differential Algebras and Pure Spinor Action in IIB Superstring Sigma Models
• Non-analytic terms of string amplitudes from partial waves
• Non-BPS D-Branes in Light-Cone Green-Schwarz Formalism
• On Forms, Cohomology, and BV Laplacians in Odd Symplectic Geometry
• A New Proposal for the Picture Changing Operators in the Minimal Pure Spinor Formalism
• Pure Spinor Integration from the Collating Formula
• General fluctuations of the heterotic pure spinor string on curved backgrounds
• Y-Formalism and Curved Beta-Gamma Systems
• The Integral Form of D=3 Chern-Simons Theories Probing ${\mathbb{C}}^n/\Gamma$ Singularities
• Superstring amplitudes meet surfaceology
• Towards Pure Spinor Type Covariant Description of Supermembrane -- An Approach from the Double Spinor Formalism --
• Massless Chiral Supermultiplets of Higher Spins and the $\theta$-Twistor
• Tension between string amplitude prescriptions with presumed spacetime supersymmetry
• Symmetries of non-maximal supergravities with higher-derivative corrections
• Supersymmetric String Configurations in Ad${\mathbb{S}}_5\times {\mathbb{S}}^5$